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Scaling units with metric prefixes ... examples
The distance between here and Columbia, SC is about 107,000 meters.
What metric unit would be best suited for a distance like this?
By "best suited", we mean a
metric unit that would
represent the number without
many beginning or end
zeros. These kinds of numbers
are easier for us to remember!
A piece of chalk is 0.080 meters long. What metric unit would be best
suited for this length?
Derived Units
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- are units that are made up of combinations of metric base units with each other
and/or with prefixes
Example:
Two derived units are particularly important in introductory chemistry:
1) VOLUME
2) DENSITY
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VOLUME
H
VOLUME = L
W
H
What are the units of volume in the metric system?
W
L
LENGTH.
Base unit of length is the meter
WIDTH.
... also a length
HEIGHT.
... also a length
... but the CUBIC METER is much too large for
routine laboratory and medical work, We need
a smaller unit!
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Practical issues for volume units
- Cubic meters are too large! A meter is very similar in length to a yard, so a
cubic meter is a cube that is approximately a yard long on each side!
Cubic decimeters are given the name "liters", abbreviation "L"
In the lab, we typically need an even smaller unit than the liter,
so we use milliliters (mL)
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DENSITY
- Density is a measure of the concentration of matter; of how much
matter is present in a given space
- Density is defined as the MASS per unit VOLUME, or ...
What are the metric units of DENSITY?
We don't usually measure mass in kilograms (or volume in cubic meters) in
the lab! In fact, our lab balances can handle only 200 grams MAXIMUM!
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In the lab, we typically measure masses as grams and volumes
as milliliters, so the density unit we will use most often is:
Measuring density
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... of a liquid
1) Measure mass of
empty cylinder
2) Fill cylinder and measure
volume of liquid
3) Measure mass of filled cylinder
4) Subtract to find mass of liquid
5) Density = mass liquid / volume liquid
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...of an object
1) Measure mass
of object
2) Partially fill cylinder
with liquid, record volume.
3) Put object into cylinder, record new
volume
4) Subtract to find volume of object
5) Density = mass object / volume object
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Converting from one unit to another
We will use the method of dimensional analysis, sometimes called the factor-label
method.... or, the "drag and drop" method!
Dimensional analysis uses conversion factors to change between one unit and another
What's a conversion factor? A simple equality.
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Conversion factors in metric
In the metric system, conversion factors between units may always be made from
the metric prefixes!
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How do we actually USE a conversion factor?
Convert 15.75 m to cm
DRAG
AND
DROP!
Put what you want to cancel on
the bottom, then ...
... put what it equals on the top!
Convert 0.01893 kg to g
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Convert 14500 mg to kg
If you have TWO prefixes
in your problem, you will apply
TWO conversion factors in
your solution!
Convert 0.147 mm to
m
micro-
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Convert 38.47 in to m, assuming 2.54 cm = 1 in
Even though English units are involved, we can solve this problem the same way
we solved the previous problem where only metric units were used!
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Even if you're unfamiliar with the metric units involved in a problem, you
can still do conversions easily.
88100 kHz to MHz
0.004184 kJ to J
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Practical applications of dimensional analysis: Drug calculations.
Example: A patient is ordered 40 mg of codeine phosphate by subcutaneous
injection. 50 mg in 1 mL liquid is available. How much of this liquid should be
adminstered?
We're trying to convert the amount to be administered (40 mg) to a volume!
So what's the conversion factor?
We can use "50 mg in 1 ml" as a conversion
factor ... it tells us how many mL of
solution contain a certain amount of drug!
Hint: Conversion factors often contain words like "in" or "per"!
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Mileage
A car (averaging 17.5 miles per gallon) is
traveling 50 miles per hour. How many gallons
of gas will be used on a trip that lasts 0.75 hours?
If gas is $3.45 per gallon, what is the cost of the trip?